Question

Solve the systems of equations.
-9x+y=12
2x+4y=-28

Answer 1

2x+6y=-18
x=5y-1

Answer 2

3x+y=2
7x-4y=30

Answer 3

To solve the system of equations, we can use the method of substitution or elimination. Let's use the method of substitution.

1. Solve the first equation for y:
-9x + y = 12
y = 9x + 12

2. Substitute the value of y in the second equation:
2x + 4(9x + 12) = -28
2x + 36x + 48 = -28
38x + 48 = -28
38x = -28 - 48
38x = -76
x = -76 / 38
x = -2

3. Plug the value of x back into the first equation to find y:
-9x + y = 12
-9(-2) + y = 12
18 + y = 12
y = 12 - 18
y = -6

Therefore, the solution to the system of equations -9x + y = 12 and 2x + 4y = -28 is x = -2 and y = -6.

Answer 4

We will use the given equation x = 5y - 1 to substitute x in the first equation.

Substitute x in the first equation:
2(5y - 1) + 6y = -18
10y - 2 + 6y = -18
16y - 2 = -18
16y = -18 + 2
16y = -16
y = -16/16
y = -1

Substitute the value of y in the equation x = 5y - 1:
x = 5(-1) - 1
x = -5 - 1
x = -6

Therefore, the solution to the system of equations 2x + 6y = -18 and x = 5y - 1 is x = -6 and y = -1.

Answer 5

To solve the system of equations, we can use the method of substitution or elimination. Let's use the method of substitution.

1. Solve the first equation for y:
3x + y = 2
y = 2 - 3x

2. Substitute the value of y in the second equation:
7x - 4(2 - 3x) = 30
7x - 8 + 12x = 30
19x - 8 = 30
19x = 30 + 8
19x = 38
x = 38 / 19
x = 2

3. Plug the value of x back into the first equation to find y:
3x + y = 2
3(2) + y = 2
6 + y = 2
y = 2 - 6
y = -4

Therefore, the solution to the system of equations 3x + y = 2 and 7x - 4y = 30 is x = 2 and y = -4.